A numerical model for the prediction of movement of gas condensate from spill accidents in the...

Indian Journal of Marine Sciences

Vol. 37(3), September 2008, pp. 233-242

A numerical model for the prediction of movement of gas condensate from spill

accidents in the Assalouyeh marine region, Persian Gulf, Iran

Habibi. S1, Torabi Azad. M

2 & Bidokhti. A.A

*3

1Islamic Azad University, Science & Research Branch, Tehran, Iran

2Physical Oceanography Dept. Islamic Azad University, North Tehran Branch, Tehran, PO Box 19735-181, Iran

3Institute of Geophysics, University of Tehran, Tehran, PO Box 14155-6466, Iran

*[E-mail: [email protected]]

Received 14 February 2007, revised.12 October 2007

This paper presents a three-dimensional numerical model of flow and movement of gas condensate spills based on

Navier-Stokes and continuity equations with Boussinesq approximation involving various surface wind forcings. The model

simulates the surface movement of gas condensate slick from spill accidents in Assalouyeh marine region. For the advection

term an upwind weighted, multidimensional positive definite advection transport algorithm (MPDATA) was used. This

algorithm uses an explicit finite difference scheme with an antidiffusive velocity for equilibrium diffusion. It also uses a

generalized-conjugate-residual (GCR) method for the solution. The model is run for gas condensate spill accidents in

Assalouyeh marine region in summer and winter of 2005. Numerical results show that gas condensate particles spread

torwards the shore in summer, while in winter it mostly spreads towards east. The spreadings follow the flow fields that are

in good agreement with flow field observations. Diffusion of gas condensate particles in the water due to more turbulence in

winter is larger, while gas condensate particles are observed on the water surface due to more stability and buoyancy force

in summer.

[Keywords: Gas condensate, concentration of particles, Assalouyeh marine region, Iran, numerical model, oil spill]

Introduction

The gas condensate spill accident is very harmful to

the marine environment as its particles can stay in the

water column for long times and pollute the deeper

water environment. In the last two to three decades

many researchers have studied the transport and the

processes of oil spills based on the trajectory method

and mass balance approachs, and various oil spill

models have been developed1-4.

In 1993, mathematical and empirical models for

surface oil spill transport in the Persian Gulf was

developed by Al-Rabeh et al

5. In these models, known as

GULFSLIK II, spreading of a surface oil spill was

simulated using the drifting buoys data of the Mt.

Mitchell Cruise, and also an empirical formula based on

the drift factor approach to estimate the surface oil spill

transport at 24-h intervals due to wind, is derived. The

empirical formula included the wind and current drift

factors approach that was based on the assumptions that

the effects of wind and current on a surface spill act

independently and can therefore be described as a vector

sum of velocities. The wind-induced oil spill speed is

also a small fraction of the wind speed. Moreover, the

direction of the oil spill motion is at a non-zero angle

(deflection angle) to the direction of the wind due to

Coriolis force. Surface currents for the specific wind

conditions were obtained from a hydrodynamic model

of the Gulf, known as HYDRO I. GULFSLIK II model

ignores tidal and density driven currents and also it is

assumed that surface oil spills move at the same velocity

as the wind driven surface currents. Results of the

drifting buoys experiments carried out in the Persian

Gulf during the Mt. Mitchell Cruise was used to estimate

wind–induced surface current speeds and the associated

directions.

A semi-analytical model of the rate of oil spill

disappearance from seawater for Kuwaiti crude and

its products has been developed by Riazi & Edalat6.

The model considers evaporation, dissolution and

sedimentation of oil components. The only adjustable

parameter in this work is a constant in the relation

between the mass transfer coefficient for evaporation

and spill size. The model estimates area, volume and

composition of oil spill versus time. It also calculates

the amount of oil vaporized, dissolved or sunk into

water with time.

Al-Rabeh et al.7 developed a the GULFSPILL

software package for the prediction of the movement

and fate of oil spills in the Persian Gulf. The package

comprises of four programs: GULFTRAK, OILPOL,

INDIAN J. MAR. SCI., VOL. 37, NO. 3, SEPTEMBER 2008

234

OILPOL-S and QUIKSLIK. In OILPOL, OILPOL-S

and QUIKSLIK the oil spill is modeled using a Monte

Carlo method. One component of the package allows

either forecasts or hindcasts of the motion of any

floating object (such as a patch of oil). The package is

based on a three-dimensional hydrodynamics model

that has been extensively tested and calibrated. The

disadvantage of this model is that the package is tied

only to one geographical location. To extend it to a

different water body would require recalibration of

the hydrodynamical model.

In the present study, a three-dimensional numerical

model is used to simulate the surface movement of

gas condensate slick from spill accident in

Assalouyeh marine region. The model is based on the

Navier-Stokes and the mass transport equations to

predict the gas condensate particles in the water

column, at the surface and also at different depths.

Assalouyeh marine region

Assalouyeh marine region is zonally at 27°30′N

and meridionally at 52°37′E (Fig. 1). The Pars Special

Economic Energy Zone (PSEEZ) has been established

in 1998 for the utilization of South Pars oil field and

gas resources. The zone is located on the northern

coastline of the Persian Gulf at 300 km to the east of

the Port of Bushehr and 570 km to the west of Port of

Bandar Abbas and approximately 100 km from the

south Pars gas field (continuation of the Qatar,s

northern dome). The zone is bounded in the north by

Zagros mountain range, on the south by the Persian

Gulf, on the west by the area of Shirino and on the

east by the area of Chahmobarak. Gas condensate is

transferred by 30 inch line to SPM (Single Buoy

Mooring) at a distance of 3 km from shore to a

loading terminal offshore for ships .

Governing equations The relations and equations governing the

behaviour of the spill and current are given below :

Spreading

Lehr et al.8 suggested that an oil slick spreads as an

ellipse and they formulated a modified Fay-type

spreading equation considering the influences of

buoyancy and wind, according to the following1,2

:

LLtwind

UgasVgas

tgasVgas

A

maxmin)4

(3/43/13/1

40

2/13/23/2

2270

πρ

ρ

ρρ

=∆

+

∆=

…(1)

tV gasgas

L 41

313

1

76.53min

where

∆=

ρρ

and

tU windLL 4

33

495.0

minmax +=

Here A is the area of the gas condensate slick (m2),

,, and gaswgasw ρρρ−ρ=ρ∆

are densities of water and gas condensate respectively,

gasV is the total volume of the spilled gas condensate in

barrels, wind

U is the wind speed in knots, t is the time

in minutes, min

L and maxL are lengths of the minor and

major axes of elliptical slick respectively (m). The first

term on the right hand side of Eq.(1) is due to the initial

phase of the spill by buoyancy and the second term is

mainly due to the wind.

Evaporation

The evaporative amount of a given component of

oil was given by the following equations1 :

)(/ RTsi

PiXtAeKi

M = …(2)

Fig. 1 — Location of Assalouyeh marine region in Persian Gulf.

The spill size is 629.33 barrels.

HABIBI et al.: MOVEMENT OF GAS CONDENSATE

235

∑= iMiMix /where

Here iM is the amount of component i lost by

evaporation (mole), e

K is the mass transfer

coefficient of evaporation m/s, A is the area of the

gas condensate slick (m2), t is the time (s), R is the gas

constant )10206.8(35

kmolmatm −× − , T is the air

temperature above the slick (k), siPiX is partial vapor

pressure of component i . siP is the vapor pressure of

component i, iX is the component mole fraction.

Mackay & Matsugu9 proposed the following

formulation to compute the mass transfer coefficient

of evaporation ek based on the results of laboratory

experiments1 (m/h) :

cSDUwindeK67.011.078.0

0292.0−−

= …(3)

where eK is the mass transfer coefficient (m/h),

windU is the wind speed (m/h), D is the gas

condensate slick diameter (m), cS is the Schmidt

number which represents the surface roughness. Then

the rates of evaporation can be calculated as1 :

∑ ∑== )(// RTsiPixAeKtiMeS …(4)

Dissolution

The amount of component i lost by dissolution can

be calculated by the following equation1 :

iSiXtAd

Ki

dM = …(5)

where i

dM is the amount of component i lost by

dissolution (mole), d

K is dissolution mass transfer

conefficient, iX is the component mole fraction, A is

the area of the gas condensate slick (m2), t is the time

(s), iS is the solubility of gas condensate.

In a report prepared by the U.S. Department of

Interior10

, the following relation is recommended to

compute d

K [Ref. no.6]:

L

D

D

w

w

Lwater

u

dK ν

ν

ν

ν

33.0

8.0035.0

= …(6)

where wν is the kinematic viscosity of seawater, νD

is the diffusion coefficient of gas condensate in water,

wateru is the water velocity and L is the square root

of surface area A. The rates of dissolution were then

calculated as1 :

∑ ∑== iSiXAd

Kti

dM

dS / …(7)

Vertical dispersion

The gas condensate slick on the sea is also subject

to the action of waves, especially breaking waves and

upper layer turbulence. Under their actions, the

coherent gas condensate slick will break up and

become small particles, then advect and diffuse in the

water column. Total mass of dispersed droplets

smaller than maxd is given by1,11

:

7.1maxcov

57.0)()( dSBA

DoCedtotM = …(8)

[ ] andwhere1

)()(−

≈ gasToC µ

20034.0 rmsHgwBA

D ρ=

Here )( edtotM is total mass of dispersed droplets

smaller than maxd )(2

m

kg, )(oC is a proportionality

constant dependent on the gas condensate viscosity

(µ) at gas condensate temperature gasT (k), BA

D is

the average energy dissipation per unit surface area in

an overturning wave, rmsH is the root mean square

value of the wave height, g is the acceleration due to

gravity, covS is the fraction of the sea surface

covered by gas condensate, maxd is maximum

droplet size and wρ is the density of water.

Conservation equations Momentum and continuity and gas condensate

particle transport equations are as follows :

Momentum equations in the yx , and z directions

are given by1 :

∂

∂

∂

∂+

∂

∂−=

∂

∂+

∂

∂+

∂

∂+

∂

∂

x

U

hxx

p

z

UW

y

UV

x

UU

t

Uν

ρ1

fVzx

y

U

hy+

∂

∂+

∂

∂

∂

∂+

)(1 τ

ρν …(9)


236

y

p

z

VW

y

VV

x

VU

t

V

∂

∂−=

∂

∂+

∂

∂+

∂

∂+

∂

∂

ρ1

fUz

y

y

Vhyx

Vhx

−∂

∂+

∂

∂

∂

∂+

∂

∂

∂

∂+

)(1 τ

ρνν …(10)

z

P

z

WW

y

WV

x

WU

t

W

∂

∂−=

∂

∂+

∂

∂+

∂

∂+

∂

∂

ρ1

gz

Wv

vzy

W

hyx

W

hx−

∂

∂∂∂+

∂

∂

∂

∂+

∂

∂

∂

∂+

νν …(11)

and the continuity equation :

0=∂

∂+

∂

∂+

∂

∂

z

W

y

V

x

U …(12)

Gas condensate particle transport equation is1 :

∂

∂

∂

∂=

∂

∂+

∂

∂+

∂

∂+

∂

∂

x

Cx

Dxz

CW

y

CV

x

CU

t

C )()()(

∑+∂

∂+

∂

∂

∂

∂+

∂

∂

∂

∂+

S

z

Cf

w

z

Cz

Dzy

Cy

Dy

)( …(13)

w

dg

w

gasw

fw

νρ

ρρ 2

18

1where

−=

Here U, V and W are the velocity components in the

longitudinal )(x , lateral )( y and vertical )(z

directions respectively, t is the time, ρ is the density

of gas condensate-water flow, P is the time–

averaged pressure, g is the gravitational acceleration,

hν is the coefficient of horizontal eddy viscosity, νν

is the coefficient of vertical eddy viscosity, xτ and

yτ are the horizontal shear stresses resulting from

vertical turbulent momentum transport, f is the

Coriolis parameter )sin2( φω=f , where ω is the

angular speed of the Earth's rotation and φ is the

geographical latitude), C is the concentration of gas

condensate particles, xD , yD and zD are the

diffusion coefficients in the yx, and z directions

respectively, s∑ is the effective source term, f

w is

the buoyant velocity of the gas condensate particles,

wρ and gasρ are the mass densities of water and

gas condensate respectively, d is the averaged gas

condensate particle size and wν is the kinematic

viscosity of water.

The density ( wgas,ρ ) and the viscosity ( wgas,ν )

are distinguished by the fraction of the gas condensate

in the gas condensate-water mixture flow and they are

defined as1 :

),1(,, wwgasFgaswgasFwgas

ρρρ −+= …(14)

wvwgasFgasvwgasFwgas

),1(,,−+=ν …(15)

where wgasF , is the fraction of the gas condensate in

the mixture, wgas,ν is kinematic molecular viscosity

of mixture, gasν is gas condensate viscosity, wν is

water viscosity, wgas,ρ is density of mixture, wρ is

water density, gasρ is gas condensate density.

The surface wind stress is computed using the

quadratic relationship :

windUV windUwindad

Csx2

1)

22( += ρτ (16)

windVV windU windad

Csy2

1)

22( += ρτ …(17)

where sxτ and syτ is surface wind stress, aρ is

density of air, d

C is drag coefficient, wind

U and

windV are components of wind velocity 10 m above

the sea surface.

For wind speeds below 25 m/s, d

c is given by the

expression :

310)21

)22

(066.063.0( −++= V windUwinddC …(18)

The bottom stress is computed using the quadratic

relationship with the depth-integrated current :

waterUV waterU waterKWbx

21

)22

( += ρτ …(19)

waterVV waterU waterKwby

21

)22

( += ρτ …(20)

where bx

τ and by

τ is bottom friction, K is bottom

friction coefficient ( K =0.002) and waterU and

waterV are components of the depth–integrated

current.


237

The horizontal mixing coefficients are given as2,13

:

2/1

2

2

5.0

2

∂

∂+

∂

∂+

∂

∂+

∂

∂

∆∆==

y

V

y

U

x

V

x

U

yxsaCyDxD

…(21)

where saC is an arbitrary constant of order 0.5 and

yx ∆∆ and are the model grid lengths in the x and

y directions.

The vertical mixing coefficient zD can be

expressed in terms of turbulent eddy viscosity and the

mixing length turbulent closure1,2

:

z

t

zz

ezD

ϕσ

ν

ϕσν

ϕσ

ν+== …(22)

,2wherez

Umlt ∂

∂= ρν

5.0)1( −+= iRmgasl

ml β

,5.0)/1(7.0 Hzzmgasl −=

and2)/(

/

zU

zgiR

∂∂

∂∂−=

ρ

ρ

5.0)101(

5.1)33.31(

iR

iR

o

z

+

+=

ϕσ

ϕσ

where mgasl is the natural mixing length and it is

simply a function of the relative depth

H

Z, tν and

ν are the coefficient of kinematic turbulent viscosity

and kinematic molecular viscosity of mixture, ml is

mixing length in the gas condensate-water flow,

20=β , iR is Richardson number, zϕσ is the

turbulent Schmidt number, 1=oϕσ and eν is

kinematic effective viscosity1.

The model assumptions The salinity and heat budget equations are not used

in the model as the water column is assumed

homogeneous. The momentum equations in the

yx , and z directions without hydrostatic

approximation are used. The prevailing wind is

assumed to be northwest. In the first stage, the shape

of gas condensate slick is assumed to be elliptical and

homogeneous. The gas condensate is assumed to be a

single component and the density of the gas

condensate and water mixture is variable.

Initial conditions and the spill parameters

Elevation of the sea surface and water velocity

everywhere is zero, except along the open boundary

of the computational domain. Vertical velocity is zero

at side boundaries and bed and in the open boundaries

they are given by the tidal informations. An idealized

seawater basin consists of 67.5×27 km2 area grided

with the grid size 300=∆=∆ yx m of in horizontal

and 20 layers in vertical, and the time step for

integration is typically 5 s.

Parameters for gas condensate are:

3

750m

kggas =ρ , kinematic viscosity is 1.15 cP,

molecular weight is 150 gr/mol, interfacial tension is

20 dyne/cm, vapour pressure is 0.35 atmosphere in

winter and 0.54 atmosphere in summer, solubility is

18 mg/l and API is 57.17.

Other parameters are :

The Schmidt number is 23.33, the diffusion

coefficient of gas condensate in water is 0.0126 m2/s,

intrusion depth is 3 m, breaking wave height is 2 m,

breaking depth is 2.56 m, significant wave height is

1.62 m, root mean square wave height is 1.412 m,

wρ is 1027 3m

kg , water viscosity is 1 cP.

Boundary conditions

At coastal boundary, the normal component of

velocity is zero. At open boundaries, the sea surface

elevation is set equal to tide table data. The entire

coastal boundary consists of a shoreline with no river

inflows. There is no inflow or outflow in coastal

boundary, as it is impermeable. There is also no-slip

condition at the coastal boundaries and at the sea bed.

Grid domain , spill size and wind condition A regular rectangular mesh (67.5×27 km

2) with

grid size 300=∆=∆ yx m and with 20566 grid in

computational domain (27°21′N, 52°50′E) is used and

it is located between Taheri Port in west and Teben in

East, (Fig. 1). The model uses topographically

following σ -coordinate in vertical. For this domain

we use 20 layers of 0.05 σ each. σ is given by :


238

hH

hzH

−

−=σ …(23)

where H is the height of the model top, h is the

height of the local topography and z is the vertical

coordinate from the bed. Total volume of the spilled

gas condensate is 629.33 barrels. An accidental spill

at 10 in the morning, on 7th Feb. 2005 and 7th July

2005 near floating bouy (SPM) 3 km from shore

(shipsloading area ) was assumed to happen. Mean

temperature and maximum wind speed were 24.9°C

and 6.455 m/s respectively in winter(on 7th Feb.

2005). Mean temperature and maximum wind speed

were 38.4°C and 5.74 m/s respectively in summer

(on 7th July 2005). Figure 2 shows the seabed

topography of Assalouyeh Marine Region.The water

depth ranges from 1 m to 72 m.

The model algorithm The model uses Boussinesq approximation as Lipps

equations without the use of hydrostatic pressure

equation14

. Algorithm for advection equation is the

multidimensional positive definite advection transport

algorithm (MPDATA)15,16

. MPDATA is based on the

upstream scheme, an iterative method based on the

antidiffusive velocities is applied to correct the

excessive numerical diffusion in such scheme. First,

the advection of a quantity is solved by means of an

upstream scheme. This is the first iteration in the

MPDATA scheme. Second, the excessive numerical

diffusion produced by such scheme is corrected

reapplying the scheme, but now one substitutes the

velocity field by introducing an antidiffusive velocity

field. The antidiffusive velocity is derived analytically

based on the truncation error analysis of the upstream

scheme. A nonoscillatory option can be applied to the

MPDATA scheme to assure monotonicity. Such

procedure may be repeated by any optional number of

times. For two iterations, the MPDATA is a second-

order-accurate in time and space for any advective

velocity field. The properties of this scheme are:

stability, consistency and conservation of positive

definitives15,16

.

Model programming

Model programming has been done in fortran

language and the program is run on a personal

computer in which the processor speed is around 3

GHz with Ram capacity of 2 GB. For time step of five

second the repeated calculation is 40000 times for

every run.

Some Observations

The current speeds at depth of 5, 10 and 15 meters

from the water surface17 for 25th Jan. 2005 in Taheri

Port (27°30′, 52°35′E) is shown in Table 1. The winds

in winter are predominantly from northwest, along the

axis of the Persian Gulf basin. We did not have any

observations in summer.

Model results Figure 3A and B show the surface current vectors

after 14 and 42 hrs predictions for the 7th Feb. 2005

Fig. 2 — The seabed topography of Assalouyeh marine region.

Table 1 — Observations results of current speed (m/s) in Taheri

Port in winter (27°30'N, 52°35'E)

Observation

(15 m from the

water surface)

Observation

(10 m from the

water surface)

Observation

(5 m from the

water surface)

Time

(hour)

0.1798 0.0987 0.1076 0

0.073 0.0923 0.1082 1

0.1318 0.0712 0.0814 2

0.0924 0.0654 0.0537 3

0.1417 0.0394 0.0782 4

0.0717 0.0339 0.0602 5

0.0532 0.0399 0.0627 6

0.0228 0.0797 0.0529 7

0.0439 0.0301 0.0826 8

0.107 0.0663 0.0658 9

0.0277 0.1023 0.0506 10

0.0893 0.0616 0.078 11

0.0915 0.0475 0.0658 12

0.1014 0.0291 0.0439 13

0.1789 0.0772 0.0443 14

0.0401 0.0617 0.019 15

0.0669 0.1117 0.0279 16

0.0381 0.0839 0.0942 17

0.149 0.1796 0.2556 18

0.2331 0.2187 0.146 19

0.2392 0.1795 0.1663 20

0.1971 0.2316 0.2938 21

0.2038 0.2666 0.3066 22

0.2744 0.2655 0.1628 23


239

with synoptic and tidal forcings for typical winter

time, as the northwesterly winds are strong. North–

westerly wind which is typical of winter time,

produces south–eastern currents, and also currents

along the coast. A region of flow divergence in east–

west direction in the middle of the region is apparent.

A cyclonic circulation also appears to develop in the

northern part of the region.

The predictions of surface concentration from the

scenario for gas condensate spill, which is released

3 km from the shore, are shown in Fig. 3C and D. The

flow field, especially the divergent region appears to

break the spill into two parts, one is moving north

towards the coast and the other is moving south–east

approaching the coast further east. In these shallow

waters towards the coast, turbulence as a result of

wave breaking can break up the gas condensate

further into smaller patches, although the model

results show an overall concentration after 14 and

42 hours in these figures. Figure 4A and B show the

corresponding flow field at a depth of about 15 m

below the surface. The flow at this depth is reverse to

that of the surface (Fig. 3A) especially in the

northwest, this maybe due to continuity and

restrictions of flow near the coastal area. The

divergent region near the middle of the region is still

marked. Also the cyclonic flow pattern in the northern

part is more dominant. Tidal forcing appears to

produce strong currents at this depth, while surface

currents are influneced by wind forcing.

Figure 4C and D show the corresponding pattern

and concentration of the gas condensate spill at a

depth of about 15 m below the surface. The size of the

spill at this depth is smaller and in one piece. At this

depth it appears to move towards east embracing the

coastal boundary. The Naiband bay appears to have

been engulfed by the gas condensate slick, and part of

the slick is observed in the north west of the spill

region. In winter time as the cold northwesterly winds

are strong more turbulent mixing and convection are

expected and the water column is almost uniform in

T , S and density (Fig. 5A , B for Leg 1 and Leg 6,

Fig. 4 — Velocity vectors of current at the depth of 15 meters

from the water surface (m/s); A) 14 hours after the accident of

spill, the value shown in the legend represents maximum speed

0.613 m/s; B) 42 hours after the accident of spill, the value shown

in the legend represents maximum speed 0.495 m/s in winter.

Concentration distribution of gas condensate particles (kg/m3) at

the depth of 15 meters from the water surface; C) 14 hours after

the accident of spill; D) 42 hours after the accident of spill in

winter.

Fig. 5 — A) Tempreature profiles for winter and summer times;

B) Salinity profiles for winter and summer ( Station 63 Mt.

Mitchell data, Reynolds, 1993. This station is near the Assalouyeh

marine region.).

Fig. 3 — Velocity vectors of current near the water surface (m/s);

A) 14 hours after the accident of spill, the value shown in the

legend represents maximum speed 0.227 m/s; B) 42 hours after

the accident of spill, the value shown in the legend represents

maximum speed 0.593 m/s in winter. Concentration distribution

of gas condensate particles (kg/m3) near the water surface; C) 14

hours after the accident of spill; D) 42 hours after the accident of

spill in winter.


240

Reynolds18). Convective condition, as flowing cold

air warms the surface water could also be expected

that may increase the spread of the spill at deeper

layers. In summer the thermocline is well developed

(Fig. 5A , B).

Mean, maximum and minimum of concentration of

hydrocarbon from model are about 17.48, 56.67 and

4.33 µg/g(ppm) respectively. Mean, maximum and

minimum of concentration of hydrocarbon, measured

by N.Ghaemi19 are 20.436, 49.309 and 3.781

µg/g(ppm) respectively.

The same spill was assumed to occur again but this

time on the 7th

July 2005 ( summer) (Fig. 1). This time

the prevailing northwesterely wind was weak and the

influence southwest monsoon in early summer leads

to surface currents moving towards the coast. Figure

6A and B show south and southeast weak currents in

the west of the region and northwesterly currents in

the east of the region and also no cyclonic circulation

was observed in the north as in the winter case. The

region of diverging flow in the surface was still

observed in a narrow band of east-westerly direction.

The flow field causes spread of gas condensate slick

near the water surface 14 and 42 hours after accident,

(Fig. 6C, D). These figures show the distribution of

particles after 14 and 42 hours due to south and

southeast currents and northwest surface current and

return current toward the northwest at the depth of

15 m from the surface, (Fig. 7A, B). Figure 6B shows

existence of south and southeast currents near the

surface.

The gas condensate slick this time appears to be

intact (in one piece) and more north. The surface area

of the slick spreads in size much less than that for the

winter case. This expected as the wind forcing is

much less in summer time. Also the thermocline

develops very markedly in summer time, so vertical

profiles of T , S and density also show strong

variations in the water column, in this area (Fig. 5A,

B). In this model we did not consider the vertical

variations of physical parameters in the water. This

may influence the vertical intrusion of the slick

towards deeper water. This may introduce some error

in predicted concentration, especially further away

offshore. Near the shore as waves are breaking,

vertical mixing is ensured, hence as the patch of the

spill reaches the near shore region it can extend to

deeper part as indicated in Fig. 7A-D which are for

the current predictions as well as the fate of the gas

condensate spill after 42 hours from the initial stage.

In fact the horizontal extent of the spill at 15 m depth

appears to be larger than that of the surface, near the

shore areas.

Figure 8A shows the thickness of the gas

condensate spill with time for summer and winter

cases. Firstly, the overall thickness for winter is less

than that for summer. Two stages of thickness

variation with time was observed, the early stage is

short and is more influenced by buoyancy which leads

to faster spreading (up to about 10 hours), then the

second stage which is mainly wind driven and slower.

Figure 8B shows the corresponding area of the spill

with time and again shows the same behaviour but in

reverse with thickness (Fig. 8A). This kind of

behaviour is also expected from Equation (1).

Fig. 6 — Velocity vectors of current near the water surface (m/s);

A) 14 hours after the accident of spill, the value shown in the

legend represents maximum speed 0.076 m/s; B) 42 hours after

the accident of spill, the value shown in the legend represents

maximum speed 0.26 m/s in summer. Concentration distribution

of gas condensate particles (kg/m3) near the water surface; C)

14 hours after the accident of spill; D) 42 hours after the accident

of spill in summer.

Fig. 7 — Velocity vectors of current at the depth of 15 meters

from the water surface (m/s); A) 14 hours after the accident of

spill, the value shown in the legend represents maximum speed

0.228 m/s; B) 42 hours after the accident of spill, the value shown

in the legend represents maximum speed 0.331 m/s in summer.

Concentration distribution of gas condensate particles (kg/m3) at

the depth of 15 meters from the water surface; C) 14 hours after

the accident of spill; D) 42 hours after the accident of spill in

winter.


241

Figure 8C and D also show the percentage of the slick

which is respectively evaporated and dissolved. The

evaporation is much more in summer than winter

time, as the temperature is high. The same is not true,

for dissolution which may be the result of more

turbulence (stronger winds) in winter. Again two

stages of the rates of evaporation and dissolution were

observed corresponding to two stages of area growth

of the spill. Figure 9 shows effect of wind in

evaporation during summer. Evaporation is more in

windy condition as expected.

Discussion A 3-D flow and gas condensate trajectory and fate

models have been made to predict the movement of a

gas condensate slick and the concentration

distribution of gas condensate particles in the water

column and also the advection, evaporation and

dissolution on the water surface. The flow model uses

the MPDATA scheme for the advection terms and is

usually more efficient than other schemes in terms of

numerical diffusion16

. The predicted flow fields for

winter and summer period seem to follow the wind

forcing at the surface and tidal forcing in deeper parts.

A band of divergent flow was observed to be

developed in the middle of the domain in east-west

direction. This band appears to be responsible for the

split of the spill, especially in winter case. Table 2

shows comparison between current speeds at different

depth predicted by the model and observation at

Taheri port in winter. There is a good agreement

between the two.

Figure 10 also shows time variation of the currents

at two depths predicted by the model and

observations. Again good agreement between the

trends are observed. However after about 15 hours,

the current speeds show large increase in the

observation, that are not shown in predicted values.

This may be due to external effects that are not

considered by the model. This indicates that may be

Fig. 8 — Comprasion of property variations of the gas condensate

slick versus time in winter and summer; A) Thickness; B) Area;

C) Evaporation; D) Dissolution.

Fig. 9 — Comparison of evaporation gas condensate slick in

summer , wind velocities 3.5 and 5 m/s.

Fig. 10 — Comparison of numerical model results and

observations mean current speed (m/s) in Taheri Port in winter

(27°40' N, 52°20'E ).

Table 2 — Comparison of numerical model results and

observations mean current speed (m/s) in Taheri Port in winter

(27°40'N, 52°20' E)

Depth (From the

water surface, m) Numerical model Observations

5

10

15

0.0273

0.02905

0.056

0.0277

0.0291

0.069

15

(After 7 hours) 0.063 0.076

15

(After 14 hours) 0.053 0.069


242

one has to extend the area of computation that is

limited by the computing power for the present study.

It can be observed that the gas condensate slick

thickness decreases rapidly during the initial 10 hours.

This means that the first stage of spreading occurs in a

short time and mainly gravity driven. Evaporation

leads to a very significant mass loss of the gas

condensate and it has a profound effect on density and

viscosity and other properties of gas condensate. The

rate of dissolution was 0.02-0.1% of the rate of

evaporation. This is mainly due to very low solubility

of gas condensate components in water. Existence of

buoyancy force and stratification leads to

accumulation of particles near the water surface in

summer. Particles mix in the water column due to

instability of water column in winter. Fate of the gas

condensate spill for the two scenarios indicate that in

winter time more area of the coast is affected by the

slick. During winter the strong diverging flow in the

middle appears to split the slick, one part moving

north and the other moving east, affecting much larger

area of the coast than for the case in summer time.

Further study is warranted to improve the model by

inclusion of heat and salinity budgets for the water

columns. This is particularly important for summer as

thermocline is well developed in most parts of the

Persian Gulf (Fig. 5A, B and e.g. Reynolds18

).

Inclusion of surface water breaking which can lead to

entrainment of gas condensate droplet into deeper

water may also be important. Such a model can also

be incorporated into an environmental monitoring

package to give real-time forcasts, after full

evaluations.

Acknowledgement Authors would like to thank all personals of Pars

Gas and Oil Company in section of Research and

Development for their support in this study.

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